Nonlinear plasmonics 描述光子在奈米尺度下和奈米結構交互作用下的非線性現象，
在打造 Nonlinear plasmonic devices 中扮演著重要的角色。以 Third Harmonic Generation(THG)來說，因為所有的物質皆展現三階非線性效應，因此其非線性的來源、產生的機制與形式並不十分明確。為了設計出 Third harmonic plasmon-based devices，更進一步的探討是必要的。 以 Shaped slit 作為探討的結構， 我們探討在不同形狀 Slit 下產生出的基頻電漿子波在平面介面上傳遞所產生的三倍頻之機制、及其所建構出來的 Third harmonic pattern 跟 Slit 形狀、入射光偏振態的關係。此外，我們還透過計算Local nonlinear polarization 以證明 THG 主要 Gold 來產生，並指出即使 THG 有 bulk response，但整個過程是由 surface response 主導。

Nonlinear plasmonics describes the nonlinear interaction between photon and the nanostructures, playing a vital role in the design of the nonlinear plasmonic devices. However, the
exact nonlinear source of THG and the working mechanisms are still under debate due to non-vanish third order susceptibility in all materials. To develop the third-harmonic plasmon-based devices, the deep understanding to the THG mechanisms in plasmonic structures is necessary. In this paper, we experimentally find out that the mechanisms of THG, which is generated by the fundamental harmonic surface plasmon polaritons in the shaped surface plasmon slit. Meanwhile, we also find that how the third-harmonic patterns relate to the shape of the slit and incident polarization. Despite THG is involved with bulk response, we show that the third order nonlinear process is dominated by the surface of the gold by calculating the local nonlinear polarization.

(1) J. Renger, R. Quidant, N. V. Hulst, and L. Novotny, ” Surface-Enhanced Nonlinear FourWave Mixing”, Phys. Rev. Lett. 104, 046803 (2010).
(2) Genevet, P. et al. "Large Enhancement of Nonlinear Optical Phenomena by Plasmonic
Nanocavity Gratings", Nano Lett. 10, 12, 4880-4883 (2010).
(3) Harutyunyan, H., Volpe, G., Quidant, R. & Novotny, L. "Enhancing the nonlinear optical
response using multifrequency gold-nanowire antennas", Phys. Rev. Lett. 108, 217403
(2012).
(4) Aouani, H., Rahmani, M., Navarro-Ca, M. & Maier, S. A. "Third-harmonic-upconversion
enhancement from a single semiconductor nanoparticle coupled to a plasmonic antenna",
Nat. Nanotechnol. 9, 1–5 (2014).
(5) Pu, Y. et al. "Nonlinear Optical Properties of Core-Shell Nanocavities for Enhanced SecondHarmonic Generation", Phys. Rev. Lett. 104, 207402 (2010).
(6) Utikal, T. et al. "Towards the origin of the nonlinear response in hybrid plasmonic systems",
Phys. Rev. Lett. 106, 133901 (2011).
(7) Metzger, B. et al. "Third harmonic mechanism in complex plasmonic Fano structures",
ACS Photonics 1, 471–476 (2014).
(8) Palomba, S. & Novotny, L. "Nonlinear excitation of surface plasmon polaritons by fourwave mixing", Phys. Rev. Lett. 101, 056802 (2008).36
(9) D. Wolf, T. Schumacher & M. Lippitz, "Shaping the nonlinear near field", Nat. Comm. 7,
10361 (2016).
(10) De Hoogh, A. et al. "Harmonics generation by surface plasmon polaritons on single
nanowires", ACS Photonics 3, 1446-1452 (2016).
(11) T.-Y. Chen et al. "Modal symmetry controlled second-harmonic generation by propagating
plasmons", Nano Lett. 19, 9, 6424-6428 (2019).
(12) Junjun Shi et al. "Efficient second darmonic generation in a hybrid plasmonic waveguide
by mode interactions", Nano Lett. 19, 6, 3838-3845 (2019).
(13) Gorodetski, Y. "Tracking surface plasmon pulses using ultrafast leakage imaging", Optica,
16, 2334-2536 (2016).
(14) Boyd, R. W. "Ch1: Third order susceptibility, CH2: Phase mismatching, CH4: Third order
susceptibility for THG", 3rd edn.
(15) Novotny, L., Hecht, B. "Ch12 - Surface Plasmons, Principles of Nano-Optics", 2rd edn.
(16) Stockman, M. I. "Nanofocusing of optical energy in tapered plasmonic waveguides", Phys.
Rev. Lett. 93, 137404 (2004).
(17) O. E. Alon, V. Averbukh, and N. Moiseyev, Phys. Rev. Lett. 80, 3743 (1998).
(18) Chen S, Li G, Zeuner F, et al., Phys Rev Lett 113, 033901 (2014).